>3 sigmas is called evidence. >5 sigmas would be called discovery. This is the standard particle physics convention. 3 sigmas also seems to be the unofficial limit after which you are allowed to get a little excited and start to speculate about the explanations. :) As the paper says the 3.4 sigmas corresponds to a p value of 6.9 x 10^-4, which means that supposing only stuff included in the Standard Model exists, getting these results (or something even stronger) just by chance has the probability of 6.9 x 10^-4. That doesn't pop the champagne yet, but it's definitely something to talk about.
